Because if I use Log::Any for production, I can use any adapter for consumption, meaning I can swap out or override easily. Also because most of the CPAN modules I like use Log::Any so I can control output from them in my own logging framework.

Also note that I only gave Log::Dispatch as an example of an adapter, one that can multiplex. Normally you only need to load Log::Any and can use the default adapters that are provided with the companion Log::Any::Adapter.